## Abstract

We study the existence of general finite-dimensional compensators in connection with the H^{∞}-optimal control of linear time-invariant systems on a Hilbert space with noisy output feedback. The approach adopted uses a Galerkin-type approximation, where there is no requirement for the system operator to have a complete set of eigenvectors. We show that if there exists an infinite-dimensional compensator delivering a specific level of attenuation, then a finite-dimensional compensator exists and achieves the same level of disturbance attenuation. In this connection, we provide a complete analysis of the approximation of infinite-dimensional generalized Riccati equations by a sequence of finite-dimensional Riccati equations. As an illustration of the theory developed here, we provide a general procedure for constructing finite-dimensional compensators for robust control of flexible structures.

Original language | English (US) |
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Pages (from-to) | 1095-1100 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 2 |

State | Published - 1999 |

Externally published | Yes |

Event | The 38th IEEE Conference on Decision and Control (CDC) - Phoenix, AZ, USA Duration: Dec 7 1999 → Dec 10 1999 |

## ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization